Nontrivial classes in $H^{\ast }(Imb(S^1,{\mathbb{R}}^n))$ from nontrivalent graph cocycles

We construct nontrivial cohomology classes of the space $Imb(S^1,{\mathbb{R}}^n)$ of imbeddings of the circle into ${\mathbb{R}}^n$, by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we construct, for every even number $n\ge 4$, a de Rham cohomology class on $Imb(S^1,{\mathbb{R}}^n)$. We prove nontriviality of these classes by evaluation on the dual cycles.